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14 days ago

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The time it takes a spinner to stop completely is 12 seconds. If the spinner completes 6 revolutions in this time, what was the

average angular velocity of the spinner, in radians per second, for the 12-second interval?

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A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units

PIT_PIT [12445]

Step $1$

Calculate the volume of a cylinder

We understand that

the volume of a cylinder can be expressed as

$V1=\pi r^{2} h$

In this scenario

$r=8\ units \\ h=15\ units$

Insert the values

$V1=\pi 8^{2} 15$

$V1=960\pi\ units^{3}$

Step $2$

Calculate the volume of a cone

We are aware that

the volume of a cone equals

$V2=\frac{1}{3}\pi r^{2} h$

In this example

$r=8\ units \\ l=17\ units \\ h=?$

Use the Pythagorean Theorem to determine the height h

$h^{2} =l^{2}-r^{2}\\ h^{2} =17^{2}-8^{2}\\ h^{2}=225\\ h=15\ units$

$V2=\frac{1}{3}\pi 8^{2} 15\\ \\ V2=320\pi \ units^{3}$

Step $3$

Calculate the empty volume inside the cylinder

$V1-V2=960\pi -320\pi =640\pi \ units^{3}$

Thus

the final result is

the empty volume inside the cylinder is $640\pi \ units^{3}$

6 0

3 months ago

Read 2 more answers

12x+7<−11 AND5x−8≥4012

Svet_ta [12734]

Answer:

No solution

Step-by-step explanation:

Given: $12x+7$ and $5x-8\geq 40$

Handle each inequality separately.

$12x+7$ Utilizing the subtraction property of inequalities

$12x$

$12x$

$x$

$x$

and

$5x-8\geq 40$ Utilizing the addition property of inequalities

$5x\geq 40+8$

$5x\geq 48$

$x\geq \dfrac{48}{5}$

Thus, the solution to the combined inequality is the overlap of both solutions.

Refer to the attached image for the number line representation.

No solution

8 0

4 months ago

Read 2 more answers

Steve can wash, fold, and iron a basket of laundry in two hours and prepare a meal in one hour. His roommate Mike can wash, fo

lawyer [12517]

Steve possesses an absolute advantage in laundry while Mike holds the comparative advantage in meal preparation.

7 0

2 months ago